Finite-dimensional collisionless kinetic theory

TL;DR

This paper presents a method to discretize collisionless kinetic plasma models into finite-dimensional Hamiltonian systems while preserving their fundamental structure, demonstrated through relativistic and gyrokinetic examples.

Contribution

It introduces a general discretization approach that maintains the Hamiltonian structure of collisionless kinetic models, applicable to complex plasma systems.

Findings

Finite-dimensional Hamiltonian systems approximate original models.

Discretization preserves key geometric properties.

Applied to relativistic Vlasov-Maxwell and gyrokinetic systems.

Abstract

A collisionless kinetic plasma model may often be cast as an infinite-dimensional noncanonical Hamiltonian system. I show that, when this is the case, the model can be discretized in space and particles while preserving its Hamiltonian structure, thereby producing a finite-dimensional Hamiltonian system that approximates the original kinetic model. I apply the general theory to two example systems: the relativistic Vlasov-Maxwell system with spin, and a gyrokinetic Vlasov-Maxwell system.